Question: Rewrite as a simplified fraction. ${2.5\overline{10} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2510.101...\\ 10x &= 25.101...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2485}$ ${x = \dfrac{2485}{990}} $ ${x = \dfrac{497}{198}} \text{or} {2 \dfrac{101}{198}}$